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A378772
Number of weakly decreasing sequences of positive integers [p1, p2, ..., p_k] satisfying n = (1 + p1*(1 + p2*(... (1 + p_k) ...))).
1
1, 1, 2, 2, 3, 2, 5, 2, 4, 4, 5, 2, 8, 2, 6, 6, 6, 2, 8, 2, 9, 8, 6, 2, 10, 5, 5, 6, 10, 2, 17, 2, 7, 7, 5, 9, 14, 2, 6, 8, 13, 2, 15, 2, 9, 14, 7, 2, 15, 7, 11, 6, 12, 2, 14, 9, 14, 8, 5, 2, 22, 2, 8, 14, 11, 11, 18, 2, 10, 8, 18, 2, 19, 2, 5, 14, 10, 11, 19
OFFSET
1,3
LINKS
EXAMPLE
a(7) = 5: [6], [3,1], [2,2], [2,1,1], [1,1,1,1,1,1] or (1+6), (1+3*(1+1)), (1+2*(1+2)), (1+2*(1+1*(1+1))), (1+1*(1+1*(1+1*(1+1*(1+1*(1+1)))))).
MAPLE
b:= proc(n, i) option remember; `if`(n=1, 1, add(
`if`(d<=i, b((n-1)/d, d), 0), d=numtheory[divisors](n-1)))
end:
a:= n-> b(n$2):
seq(a(n), n=1..100);
CROSSREFS
Sequence in context: A325339 A010846 A073023 * A173754 A180125 A342086
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 06 2024
STATUS
approved